Method for adjusting the orbital path of a satellite

ABSTRACT

A method for adjusting the path of a satellite to limit a risk of collision with items of debris each having a date of closest pass with the satellite is disclosed including: propagating at least one orbit from the reference path of the satellite according to at least one manoeuvre to the farthest date of closest pass; determining a probability of collision for each item of debris according to the at least one orbit; determining at least one overall probability according to the set of probabilities determined; selecting the lowest overall probability from among the at least one overall probability obtained; determining a command for the satellite including the manoeuvre associated with the lowest overall probability.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a method for adjusting the orbital pathof a satellite in order to reduce a probability of collision of thesatellite with a cloud of space debris. More particularly, the presentinvention relates to a method for determining one or more manoeuvres ofthe satellite orbiting the earth to reduce the probability of collisionof the satellite with the cloud of orbital debris, that is, with all theorbital debris of the cloud.

PRIOR ART

Sequential debris avoidance strategies for a satellite based on a singlemanoeuvre on the opposite side of the orbit of a piece of debris areknown in prior art. This strategy was adapted to the chemical propulsionsatellite and considering the former population of tracked debris.

The current context is marked by an increase in mega constellationprojects, where up to 1000 satellites can be operated. In addition, thenumber of tracked debris could increase from 20,000 to 100,000 objectswhen the detected radar surface of the debris is reduced from 10centimetres to 5 centimetres. These two phenomena will createmulti-debris conjunctions, where several pieces of debris have to beavoided.

In the case of electrically propelled satellites, space debris avoidancebecomes more complex than for chemically propelled satellites. This isbecause the low thrust associated with electric propulsion does notusually enable avoidance to be performed in a single manoeuvre.

In addition, due to the low thrust associated with electric propulsion,satellite station-keeping manoeuvres are much more frequent. Therefore,to avoid mission disruption, hold manoeuvres can only be located in adedicated location. In this way, hold manoeuvres will not be plannedwhen the satellite is required for other purposes. Finally, in order toavoid operators commanding all hold manoeuvres, it is essential tocalculate these hold manoeuvres with an automatic process.

To this end, sequential debris avoidance strategies by a satellite canno longer be applied.

DISCLOSURE OF THE INVENTION

The present invention aims to remedy these drawbacks with a completelynew approach.

To this end, according to a first aspect, the present invention relatesto a method for adjusting a satellite orbital path to limit a risk ofcollision with a cloud of space debris, each piece of debris including adate of closest passage with the satellite, the method including thesteps of: determining a reference path of the orbit of the satellitefrom an initial time instant until the date of closest passage furthestfrom the initial time instant; determining an ephemeris of statetransition data representative of the reference path of the orbit of thesatellite; propagating, according to the determined ephemeris of statetransition data, at least one first alternative orbit of the referenceorbit of the satellite according to at least one first avoidancemanoeuvre related to the satellite performed during at least one freemanoeuvre time slot, and from at least one manoeuvre time instant of theat least one free manoeuvre time slot until the date of closest passagefurthest from the initial time instant; analytically determining anindividual probability of collision on each date of closest passage foreach piece of debris according to the at least one first alternativeorbit of the satellite; determining at least one overall probability ofcollision according to all the individual probabilities of collisiondetermined according to the at least one first alternative orbit of thesatellite related to the at least one first avoidance manoeuvre;selecting at least one first lowest overall probability of collisionfrom the at least one overall probability obtained; determining acommand of the satellite including at least the first manoeuvre relatedto the first lowest overall probability of collision selected.

The invention is implemented according to the embodiments andalternatives set out below, which are to be considered individually orin any technically operative combination.

Advantageously, the determination of a reference path of the orbit ofthe satellite can be determined according to a free drift propagation ofthe orbit of the satellite.

Advantageously, the step of propagating at least one first alternativeorbit, the step of analytically determining an individual probability ofcollision and the step of determining at least one overall probabilityof collision, may be repeated iteratively along a plurality ofdirections of the at least one first avoidance manoeuvre so as to obtaina first plurality of alternative orbits related to a first plurality ofavoidance manoeuvres and to evaluate a first plurality of overallprobabilities of collision related to each of the alternative orbitsrelated to the first plurality of avoidance manoeuvres.

Advantageously, each avoidance manoeuvre may comprise an initial valueof maximum velocity variation allowed during the avoidance manoeuvre.

Advantageously, the method may comprise a step preceding the step ofdetermining a command of the satellite, comprising adjusting thevelocity variation of the at least one first avoidance manoeuvre of thecommand when the at least one previously selected lowest overallprobability is less than a critical probability threshold of collision,so as to obtain at least one first overall probability of collision asclose as possible to or equal to the critical probability threshold ofcollision.

Advantageously, the step of propagating at least one first alternativeorbit, the step of analytically determining an individual probability ofcollision and the step of determining at least one overall probabilityof collision can be repeated according to a plurality of free manoeuvreslots of the satellite so as to obtain a second plurality of alternativeorbits and to evaluate a second plurality of overall probabilities ofcollision related to the second plurality of alternative orbits.

Advantageously, the step of determining a command of the satellite maycomprise a step of determining at least one second manoeuvre of thecommand of the satellite, said second manoeuvre being combined with thefirst manoeuvre related to the first lowest overall probability ofcollision, the at least one second manoeuvre producing a secondalternative orbit enabling the calculation of a second lowest overallprobability of collision according to the step of propagating the atleast one first alternative orbit, the step of analytically determiningan individual probability of collision, the step of determining at leastone overall probability of collision and the step of selecting a firstlowest overall probability of collision from the at least one overallprobability obtained.

Advantageously, the determination of the second manoeuvre of thesatellite command may include the step of determining a reference pathof the orbit and the step of determining an ephemeris of statetransition data according to which the reference path of the satelliteis the path of the first alternative orbit of the satellite related tothe first lowest overall probability of collision.

Advantageously, the ephemeris of state transition data may be anephemeris of state transition matrix.

According to a second aspect, the present invention relates to acomputer program product comprising instructions which, when the programis executed by a computer, cause the computer to implement the steps ofthe method described above.

According to a third aspect, the present invention relates to aninformation storage medium storing a computer program comprisinginstructions for implementing, by a processor, the method describedabove, when said program is read and executed by said processor.

BRIEF DESCRIPTION OF THE FIGURES

Further advantages, purposes and characteristics of the presentinvention will be apparent from the following description made, forexplanatory and non-limiting purposes, with reference to the attacheddrawings, in which:

FIG. 1 is a schematic representation of a first risk of collisionsituation between a satellite orbiting the Earth and a piece of spacedebris from a cloud of space debris.

FIG. 2 is a schematic representation of a second risk of collisionsituation between the satellite orbiting the Earth and another piece ofspace debris of the cloud of space debris of FIG. 1 .

FIG. 3 is a schematic representation of an expression for an overallprobability of collision from the individual probabilities of collisionbetween the satellite and the entire cloud of debris of FIG. 1 .

FIG. 4 is a schematic representation in the form of a time graph of afree drift propagation of the reference orbit of the satellite from aninitial time instant until the date of closest passage of a piece ofdebris of the cloud with the satellite that is furthest from the initialtime instant.

FIG. 5 is a schematic representation of a satellite control centre forcommanding the satellite according to a plurality of time slots.

FIG. 6 is a schematic time representation of a plurality of avoidancemanoeuvre free time slots dedicated to the satellite, each free timeslot being associated with a maximum orbital velocity variation of thesatellite allowed during the free time slot.

FIG. 7 is a schematic representation of several examples of orbits ofthe satellite deviating from the reference orbit X_(ref) followingexamples of orbital manoeuvre operations of the satellite.

FIG. 8 is a schematic representation of an example combination of twoavoidance orbital manoeuvres associated with the satellite.

FIG. 9 is a schematic time representation of an example of multipleorbital manoeuvres of the satellite to obtain an overall probability ofcollision less than a critical threshold of collision.

FIG. 10 is a representation of an example flowchart of the method foradjusting the orbital path of the satellite.

FIG. 11 is a schematic representation of a device for implementing themethod for adjusting the orbital path of the satellite.

DESCRIPTION OF THE EMBODIMENTS

According to FIG. 1 and FIG. 2 , a satellite 10 orbiting the Earth 12and a cloud of space debris d₁, d₂, d₃, d₄, d_(i) comprising a pluralityi of space debris d₁, d₂, d₃, d₄, d_(i) also orbiting the Earth 12 arerepresented. The satellite 10 orbits the earth 12 along its referenceorbit X_(ref). Each piece of space debris d₁, d₂, d₃, d₄, d_(i) of thecloud of debris comprises its own orbital path X_(d1), X_(di). Eachpiece of space debris d₁, d₂, d₃, d₄, d_(i) is associated with anindividual probability P₁, P_(i) of collision with the satellite 12,each of the individual probabilities P₁, P_(i) of collision beingevaluated according to a date specific to each piece of debris, calledthe date of closest passage TCA₁, TCA_(i), that is, the date on whichthe distance between the average paths of the satellite 10 and eachpiece of debris d₁, d₂, d₃, d₄, d_(i) considered individually is theshortest.

It is known to evaluate an individual probability P_(i) of collisionbetween a satellite 10 and a single piece of space debris d₁ in severalways according to the thesis presented and defended on December 10, twothousand and fifteen by Romain Serra, entitled “Opérations de proximitéen orbite: évaluation du risque de collision et calcul de manoeuvresoptimales pour l'évitement et le rendez-vous”, said thesis beingpublicly accessible especially via the “archives-ouvertes.fr” websiteunder the reference tel-01261497. It will be noted in particular that aprobability P_(i) of collision between a satellite and a single piece ofdebris d₁ can be evaluated both according to a numerical integrationcalculation and according to an analytical formula in the form of aconvergent series with positive terms.

According to FIG. 3 , a method for adjusting the orbital path of asatellite in order to reduce a probability of collision of the satellitewith a cloud of space debris comprises determining the individualprobability P_(i) of collision of each piece of debris d₁, d₂, d₃, d₄,d_(i) of the cloud with the satellite 12, each individual probabilityP₁, P_(i) of collision having been evaluated according to its date ofclosest passage TCA₁, TCA_(i).

To this end, the method for adjusting the orbital path of the satellite10 requires the calculation of the probability of collision of thesatellite 10 with the entire cloud of debris d₁, d₂, d₃, d₄, d_(i). Inthe following, the probability of collision of the satellite 10 with thecloud of debris will be referred to as the overall probability P_(g) ofcollision. The overall probability P_(g) of collision according to theinvention can be determined from all the individual probabilities P₁,P_(i) of collision previously estimated, each on their date of closestpassage TCA₁, TCA_(i). Assuming that the probability calculationrelating to an overall non-collision of the satellite 10 with the cloudof debris d₁, d₂, d₃, d₄, d_(i) can be determined by the followingformula:

${1 - {Pg}} = {\prod\limits_{i}\left( {1 - {Pi}} \right)}$

the overall probability P_(g) of collision according to the invention isdetermined according to the formula:

${Pg} = {1 - {\prod\limits_{i}\left( {1 - {Pi}} \right)}}$

For the purpose of evaluating, on a given initial date t₀, theindividual probability P_(i) of collision between a satellite 10 and asingle piece of space debris d₁, it is necessary to be able to determineas precisely as possible the orbital position and the covariance of theorbital position that the satellite and the single piece of debris wouldhave on the date of closest passage TCA1 according to the data of theorbital position and the covariance of the orbital position of thesatellite and the single piece of debris on the initial date t₀.

According to the invention, it is necessary that the data on the orbitalpositions and covariance of the orbital positions of the debris d₁, d₂,d₃, d₄, d_(i) of the cloud on the date of their closest passage TCA₁,TCA_(i) with the satellite are previously known data, provided by spacedebris monitoring agencies such as, for example and in a non-limitativemanner, the American organisation CSOpC (Combined Space OperationsCenter), or the international organisation SDA (The Space DataAssociation).

According to the invention, it is necessary to determine an ephemeris ofdata enabling the propagation of a state difference, also calledephemeris of state transition data, enabling a projection of the orbitalposition X(t) and of the covariance Cov of the orbital position of thesatellite 10 on the dates of closest passages TC₁, TCA_(i).

In particular, it is possible to be able to propagate the relativemotion of a satellite using a state transition matrix.

According to FIG. 4 , one solution consists in performing a free driftpropagation of the orbit of the satellite 10, that is, withoutmanoeuvring the satellite 10, once from the initial date t₀ ofdetermination of the overall probability P_(g) of collision until thedate of closest passage TCA_(last) furthest from the initial date t₀ ofa piece of debris d₁, d₂, d₃, d₄, d_(i) of the cloud. In this respect,two ephemerides are determined, namely an ephemeris of the referenceorbit X_(ref) of the satellite 10 and an ephemeris of the statetransition matrix ϕ(t, t₀) corresponding to the path of the referenceorbit X_(ref). This determination especially makes it possible tocalculate all the state transition matrices ϕ(t_(n), t_(m)) required forthe method for adjusting the orbital path of the satellite.

According to FIG. 5 , the first satellite 10 orbiting the Earth 12 is incommunication with a control centre 14 of the satellite 10 via a radiofrequency communication means 16. The control centre 14 of the satellite10 may be configured to command orbital path manoeuvres of the satellite10 especially by commanding thrusts of the satellite 10 according to avariation of the orbital velocity ΔV of the satellite 10 in a direction{right arrow over (d)} of the thrust. According to FIG. 5 , an exampleof a period of revolution of the satellite 10 around the Earth, alsocalled the orbital period of the satellite 10 around the Earth 12, isrepresented schematically by a discontinuous circle formed by severalarcs of circle. Each arc represents a time slot that can be dedicated toan operation of the satellite 10. As a non-limiting example, andaccording to FIG. 5 , the orbital period of satellite 10 may comprisetwo time slots for charging a battery for powering the satellite 10, twoother time slots for correcting the attitude of satellite 10 ifnecessary, another time slot for a mission to photograph the Earth 12,and finally two other time slots available for any other operations ofthe satellite. In the following, the available time slots will bereferred to as free manoeuvre slots Sl₁, Sl₂.

According to the invention, the method for adjusting the orbital path ofthe satellite 10 consists in determining the manoeuvre or manoeuvresnecessary to command the satellite 10 during the free slot or slotsSl_(i), in order to simultaneously avoid all the debris d₁, d₂, d₃, d₄,d_(i) of the cloud when the initial overall probability P_(g0) ofcollision of the satellite 10 with the cloud of debris d₁, d₂, d₃, d₄,d_(i) is greater than a critical probability threshold P_(th) ofcollision; the initial overall probability P_(g0) of collision of thesatellite 10 being determined according to the reference orbit X_(ref)of satellite 10.

According to the invention, in general, the term time slot may comprisesimply an occasional date on which it is possible to command an orbitalpath adjustment manoeuvre of the satellite 10.

Known prior art enabling the determination of one or more avoidancemanoeuvres for a single piece of debris at a time is not contemplatable.Indeed, in the context of avoidance of a cloud of debris d₁, d₂, d₃, d₄,d_(i) it is not possible to determine an avoidance manoeuvre for a firstpiece of debris d₁ of the cloud without taking account of the otherdebris d₂, d₃, d₄, d_(i) of the cloud. In addition, the calculation timeof the cumulative avoidance manoeuvre for each of the debris would betoo heavy and not fast enough for the avoidance of the cloud of debrisd₁, d₂, d₃, d₄, d_(i).

According to the invention, a fast propagation based on the statetransition matrix ϕ(t, t₀) and the ephemeris of the reference orbitX_(ref) of the satellite 10 enables the calculation of the effect of amanoeuvre during any of the free manoeuvre slots Sl₁, Sl_(i) of thesatellite 10. The ephemerides will be used in the optimisation processto test a large number of possible thrust directions in order tocalculate the effect on the overall probability P_(g) of a manoeuvreduring any of the free manoeuvre slots Sl₁, Sl_(i) of the satellite 10.

The ephemerides of the orbit of the satellite 10 can be considered as areference path that does not take account of the manoeuvre underconsideration. The idea of calculating the real path is to modify thisreference path by means of the ephemerides of the state transitionmatrix ϕ(t, t₀).

To this end, the method for adjusting the orbital path of the satellite10 comprises determining a first manoeuvre ΔV.{right arrow over (d)} anda free slot Sl_(n) enabling the execution of the first manoeuvreΔV.{right arrow over (d)} so as to best optimise the overall probabilityP_(g) of collision, that is, preferably to obtain an overall probabilityP_(g) of collision less than or equal to the critical probabilitythreshold P_(th) of collision.

To this end, according to FIG. 6 , each free manoeuvre slot Sl₁, Sl_(i)is associated with a maximum velocity variation ΔV. The maximumvariation ΔVmax of the velocity may be related for example and in anon-limiting manner either to the duration of the free manoeuvre slotSl₁, Sl_(i) or to the maximum energy consumption of the electricpropulsion device of the satellite 10 allowed for a manoeuvre. It willalso be necessary according to the invention, that a minimum variationof the velocity of the satellite 10 is defined, this minimum variationbeing related to the minimum thrust energy required by the satellite 10to perform a change of orbit of the satellite 10.

According to FIG. 7 , several examples of orbits of the satellite 10deviating from its reference orbit X_(ref) as a result of manoeuvreoperations are represented. A first avoidance orbit X₁₁ of satellite 10deviating from the reference orbit X_(ref) is represented. Said firstavoidance orbit X₁₁ follows a first avoidance manoeuvre ΔV_(max1).{rightarrow over (d)}₁₁ commanded at a first manoeuvre time instant t_Sl₁associated with the first free manoeuvre slot Sl₁. The reference orbitX_(ref) of the satellite 10 before the first manoeuvre ΔV_(max1).{rightarrow over (d)}₁₁ at the manoeuvre time instant t_Sl₁ is directlydetermined according to the reference orbit X_(ref) determined at themanoeuvre time instant t_Sl₁, and denoted as X_(ref)(t_Sl₁). Moreparticularly, this orbit X_(ref)(t_Sl₁) can be determined by using thereference orbit X_(ref) by interpolating it into the generatedephemerides.

The determination of the first avoidance orbit X₁₁(t_Sl₁) evaluated atthe manoeuvre time instant t_Sl₁ following the first avoidance manoeuvreΔV_(max1). {right arrow over (d)}₁₁ can be calculated by updating thereference orbit X_(ref)(t_Sl₁) at the manoeuvre time instant t_Sl₁according to the first avoidance manoeuvre ΔV_(max1).{right arrow over(d)}₁₁. For Cartesian elements, this corresponds to performing avelocity increment ΔV_(max1) with the direction {right arrow over (d)}₁₁of the manoeuvre expressed in the reference frame associated with theseCartesian elements. For Keplerian, circular and equinoctial elements,the Gaussian equation provides this delta state. In all cases, thecalculation of the orbital deviation created by the first avoidancemanoeuvre ΔV_(max1).{right arrow over (d)}₁₁ can be written:ΔX₁₁(t_Sl₁)=F(ΔV_(max1).{right arrow over (d)}₁₁, X_(ref)(t_Sl₁)).Knowing the state transition matrices ϕ(TCA_(i), t₀) and ϕ(t_Sl₁, t₀)determined previously, the orbital deviation ΔX₁₁(TCA_(i)) of thesatellite 10 on each of the dates of closest passages TCA_(i) can bedetermined according to the formula:

ΔX ₁₁(TCA _(i))=ϕ(TCA _(i) , t_Sl ₁).ΔX ₁₁(t_Sl ₁)=ϕ(TCA _(i) ,t₀).ϕ(t_Sl ₁ ,t ₀)⁻¹.ΔX ₁₁(t_Sl ₁)

In order to be able to calculate all individual probabilities ofcollision P_(i) between satellite 10 according to its first avoidanceorbit X11 following the first avoidance manoeuvre ΔV_(max1).{right arrowover (d)}₁₁, and all debris d₁, d₂, d₃, d₄, d_(i) of the cloud accordingto their respective date of closest passage TCA_(i), it is necessary todetermine the first avoidance orbit X₁₁(TCA_(i)) on each of said datesof closest passages TCA_(i). In this respect, the reference orbitX_(ref)(TCA_(i)) can be determined on each of the dates of closestpassage TCA_(i) by interpolating this reference orbit X_(ref)(TCA_(i))into the ephemerides generated according to each of the dates of closestpassage TCA_(i). Finally, the first avoidance orbit X₁₁(TCA_(i)) on eachof said dates of closest passages TCA_(i) can be determined according tothe formula:

X ₁₁(TCAi)=X _(ref)(TCA _(i))+ΔX ₁₁(TCA _(i))

In order to be able to calculate all individual probabilities ofcollision P_(i) between the satellite 10 according to its firstavoidance orbit X₁₁ following the first avoidance manoeuvreΔVmax₁.{right arrow over (d)}₁₁, and all the debris d₁, d₂, d₃, d₄,d_(i) of the cloud according to their respective date of closest passageTCA_(i), it is necessary to determine the covariance COV_(TCAi) of theorbital position of the satellite on each of said dates of closestpassages TCA_(i). Knowing the state transition matrix ϕ(TCAi, t₀)determined previously, and the covariance COV_(t0) of the orbitalposition of the satellite 10 on the initial date ₀, the determination ofthe covariance COV_(TCAi) projected to each of the dates of closestpassage TCA_(i) is determined by the following formula:

cov_(TCAi)=ϕ(TCAi, t ₀)×cov_(t) ₀ ×ϕ(TCAi,t ₀)^(t)

The first avoidance orbit X₁₁ of satellite 10 after the first avoidancemanoeuvre ΔVmax₁.{right arrow over (d)}₁₁, being determined on each dateof closest passage TCA_(i), as well as the covariance COV_(TCAi) on eachdate of closest passage TCA_(i), the orbit of each piece of debris d₁,d₂, d₃, d₄, d_(i) and their covariance on their date of closest passageTCA_(i) being also known, the method for adjusting the orbital path ofthe satellite 10 may comprise determining all the individualprobabilities of collision P_(i) between the satellite 10 according toits first avoidance orbit X₁₁ following the first avoidance manoeuvreΔVmax₁.{right arrow over (d)}₁₁, and all debris d₁, d₂, d₃, d₄, d_(i) ofthe cloud according to their respective date of closest passage TCA_(i).To this end, the overall probability P_(g11) of collision related to thefirst avoidance manoeuvre ΔVmax₁.{right arrow over (d)}₁₁ performedduring the first free manoeuvre slot SL₁ can be calculated and comparedwith a critical probability threshold P_(th) of collision.

According to FIG. 7 , the method for adjusting the orbital path of thesatellite 10 may comprise determining the overall probability P_(g) ofcollision as a function of different directions {right arrow over (d)}of a manoeuvre performed during the same free manoeuvre slot SL₁ andaccording to a given orbital velocity variation ΔV of the satellite 10.According to FIG. 7 , a second avoidance orbit X₂₁ of the satellite 10representing an alternative to the first orbit X₁₁ is represented. Thissecond orbit, called second alternative avoidance orbit X₂₁ is obtainedafter the application of a second alternative avoidance manoeuvreΔVmax₁.{right arrow over (d)}₂₁ different from the first avoidancemanoeuvre ΔVmax₁.{right arrow over (d)}₁₁ during the same first freemanoeuvre slot SL₁. This so-called second alternative avoidancemanoeuvre ΔVmax₁.{right arrow over (d)}₂₁ differs from the firstavoidance manoeuvre ΔVmax₁. {right arrow over (d)}₁₁ in that thedirection {right arrow over (d)}₂₁ applied to the thrust of thesatellite 10 according to the same orbital velocity variation ΔV_(max1)differs from the first direction {right arrow over (d)}₁₁. In thisrespect, a second alternative avoidance orbit X₂₁(TCA_(i)) of thesatellite 10 on all dates of closest passage TCA_(i) is also determinedin the same way as described for the first avoidance orbit X₁₁(TCA_(i)).Knowing also the covariance COV_(TCAi) for each of the dates of closestpassage TCA_(i), a second alternative overall probability P_(g12) ofcollision related to the second alternative avoidance manoeuvreΔV_(max1).{right arrow over (d)}₂₁ performed during the first freemanoeuvre slot Sl₁ can be calculated and compared with the criticalprobability threshold P_(th) of collision and also with the overallprobability P_(g11) of collision related to the first avoidancemanoeuvre ΔVmax₁.{right arrow over (d)}₁₁ performed during the firstfree manoeuvre slot Sl₁.

According to FIG. 7 , the method for adjusting the orbital path of thesatellite 10 may comprise determining an overall probability P_(g) ofcollision as a function of the positioning in time of a manoeuvreΔV{right arrow over (d)}. In other words, the overall probability P_(g)of collision is also a function of the free manoeuvre slot Sl₁, Sl_(i)during which a manoeuvre is performed. According to FIG. 7 , a thirdalternative avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(1i)performed during any of the free slots Sl_(i) distinct from the firstfree slot Sl₁ of manoeuvre is represented. To this end, a thirdalternative avoidance orbit X_(1i)(TCA_(i)) of the satellite 10 specificto each of the dates of closest passage TCA_(i) is also determined inthe same way as described for the first avoidance orbit X₁₁(TCA_(i)).Also knowing the covariance COV_(TCAi) for each of the dates of closestpassage TCA_(i), a third alternative overall probability P_(g1i) ofcollision associated with the third avoidance manoeuvre ΔVmax_(i).{rightarrow over (d)}_(1i) performed during said any of the free slots Sl_(i)distinct from the first free manoeuvre slot Sl₁ can be determined andcompared with the critical probability threshold P_(th) of collision andalso with the lowest overall probability P_(g) of collision determinedduring the first free manoeuvre slot Sl₁.

In the same way as previously described, the method for adjusting theorbital path of the satellite 10 may comprise determining the overallprobability P_(g) of collision as a function of different directions{right arrow over (d)} of a manoeuvre performed during any free slotSl_(i) and according to a given orbital velocity variation ΔV of thesatellite 10. According to FIG. 7 , a fourth alternative avoidance orbitX_(2i) of the satellite 10 deviating from the reference orbit X_(ref) atthe manoeuvre time instant t_Sli representing an alternative of thepreviously described third alternative avoidance orbit X_(1i) isrepresented. This fourth alternative avoidance orbit X_(2i) is obtainedafter the application of a fourth alternative avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(2i) different from the thirdalternative avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(1i)associated with the previously described third alternative avoidanceorbit X_(1i). This so-called fourth alternative avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(2i) differs from the third alternativeavoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(1i) in that thedirection {right arrow over (d)}_(2i) applied to the thrust of thesatellite 10 according to the same orbital velocity variation ΔVmax_(i)differs from the direction {right arrow over (d)}_(1i) of the thirdalternative avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(1i).In this respect, a fourth alternative avoidance orbit X_(2i)(TCA_(i)) ofthe satellite 10 related to the fourth alternative avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(1i) is also determined on all dates ofclosest passages TCA_(i) in the same way as described for the firstavoidance orbit X₁₁(TCA_(i)). Knowing also the covariance COV_(TCAi) foreach of the dates of closest passage TCA_(i), a fourth alternativeoverall probability P_(g2i) of collision related to the fourthalternative avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(2i)performed during said any of the free slots Sl_(i) distinct from thefirst free manoeuvre slot Sl₁ can be calculated and compared with thecritical probability threshold P_(th) of collision and also with thethird alternative overall probability P_(g1i) of collision related tothe third alternative avoidance manoeuvre ΔVmax_(i).{right arrow over(d)}_(1i) performed during the same free slot Sl_(i).

According to the determination of one or more overall probabilities ofcollision P_(g) as described in FIG. 7 , under the hypothesis that atleast one of the determined overall probabilities of collision P_(g)would be less than or equal to the critical probability threshold P_(th)of collision, then a single avoidance manoeuvre ΔVmax.{right arrow over(d)} performed during a single free slot Sl_(i) would enable collisionavoidance of the satellite 10 with all the debris d₁, d₂, d₃, d₄, d_(i)of the cloud. According to this hypothesis, several strategies of themethod for adjusting the orbital path of satellite 10 are possible.

A first strategy may consist in determining the first manoeuvreΔV.{right arrow over (d)} enabling collision avoidance, that is, theavoidance manoeuvre ΔV.{right arrow over (d)} for which the overallprobability P_(g) of collision associated with this manoeuvre, and thusthe free slot Sl_(i) associated with the manoeuvre, is less than orequal to the critical probability threshold P_(th) of collision. Inorder to determine the collision avoidance manoeuvre ΔV.{right arrowover (d)}, it will be necessary, for example, to first set a parameterof orbital velocity variation ΔV of the satellite 10, for example andpreferably according to its maximum value ΔVmax_(i) allowed during thefree slot Sl_(i) under consideration and to vary the direction {rightarrow over (d)} of the manoeuvre. This operation is repeated on all theslots until a manoeuvre ΔVmax_(i).{right arrow over (d)} is obtainedthat enables an overall probability less than or equal to the criticalprobability threshold P_(th) of collision to be obtained. The choice ofthe maximum allowed value ΔVmax_(i) of orbital velocity variation is arelatively relevant choice to obtain a lower overall probability P_(g)with orbital velocity variations ΔV less than the maximum variationΔVmax_(i).

In the case of an overall probability P_(g) obtained strictly less thanthe critical probability threshold P_(th) of collision, a reduction inthe maximum velocity variation ΔV_(max) is possible in order to obtainan overall probability P_(g) of collision preferably equal to, or veryclose to, the critical probability threshold P_(th) of collision. Inthis way, the energy required for the identified manoeuvre will bereduced to a minimum.

It will be necessary according to the invention, that the determinationof an orbital velocity variation ΔV combined with a determination ofmanoeuvre direction {right arrow over (d)} can be performed, for exampleand in a non-limiting manner, by dichotomy algorithms or Brent methods.It should be noted that a velocity variation ΔV may be associated withan optimal manoeuvre direction {right arrow over (d)}.

A second strategy may consist in determining, over a free slot Sl_(i)under consideration, the avoidance manoeuvre ΔV{right arrow over (d)}enabling the lowest overall probability P_(g) of collision as a functionof all possible manoeuvre directions {right arrow over (d)}, the orbitalvelocity variation ΔV of the manoeuvre preferably also being set to themaximum velocity variation ΔVmax_(i) allowed on the free slot Sl_(i)under consideration. If the free slot Sl_(i) under consideration doesnot make it possible to obtain an overall probability P_(g) less than orequal to the critical probability threshold P_(th) of collision, thedetermination should be repeated on another free slot Sl_(i). In casethis other free slot Sl_(i) enables an overall probability P_(g) lessthan the critical probability threshold P_(th) of collision, a reductionin the maximum orbital velocity variation ΔV_(max) of the manoeuvreΔV_(max){right arrow over (d)} determined is possible in order to obtainan overall probability P_(g) of collision preferably equal to, or evenvery close to, the critical probability threshold P_(th) of collision.

A third strategy may consist in determining, over all the previouslyidentified free slots Sl_(i), the avoidance manoeuvre ΔV{right arrowover (d)} enabling the lowest overall probability P_(g) of collision asa function of all the directions {right arrow over (d)} of possiblemanoeuvres for each free slot Sl_(i), the orbital velocity variation ΔVof the manoeuvre also preferably being set to the maximum velocityvariation ΔVmax_(i) allowed for each free slot Sl_(i). Similarly to thefirst strategy, in the case where the identified avoidance manoeuvreΔV{right arrow over (d)} enables an overall probability P_(g) less thanthe critical probability threshold P_(th) of collision, a reduction inthe maximum orbital velocity variation ΔV_(max) of the manoeuvreΔV_(max){right arrow over (d)} determined is possible in order to obtainan overall probability P_(g) of collision preferably equal to, or evenvery close to, the critical probability threshold P_(th) of collision.

It is well understood that other strategies for determining a collisionavoidance manoeuvre ΔV{right arrow over (d)} according to thedescription in FIG. 7 are possible, so that the invention is not limitedto the three examples of collision avoidance strategy previouslydescribed.

According to the invention, it is also likely that a single avoidancemanoeuvre ΔV{right arrow over (d)} may not be sufficient to avoid acollision between the satellite 10 and all the debris of the cloud. Inother words, it is also likely, according to the invention, that asingle manoeuvre ΔV{right arrow over (d)} may not enable an overallprobability P_(g) of collision less than or equal to the criticalprobability threshold P_(th) of collision to be obtained.

To this end, according to FIG. 8 , a first avoidance manoeuvreΔVmax₁.{right arrow over (d)}₁₁ and a second avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(5i) of the satellite 10 following thefirst avoidance manoeuvre ΔVmax₁.{right arrow over (d)}₁₁ arerepresented, the combination of the first avoidance manoeuvreΔVmax₁.{right arrow over (d)}₁₁ with the second avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(5i) enabling avoidance of thecollision of the satellite 10 with the debris d₁, d₂, d₃, d₄, d_(i) ofthe cloud. More particularly, the first avoidance manoeuvreΔVmax₁.{right arrow over (d)}₁₁ represented is the first avoidancemanoeuvre ΔVmax₁.{right arrow over (d)}₁₁ represented in FIG. 7 forwhich a first avoidance orbit X₁₁ deviating from the reference orbitX_(ref) has been determined. It will be necessary to hypothesise that ofall the manoeuvres ΔV{right arrow over (d)} estimated in accordance withthe description in FIG. 7 , the first avoidance manoeuvre ΔVmax₁.{rightarrow over (d)}₁₁ commanded at the first manoeuvre time instant t_Sl₁associated with the first free manoeuvre slot Sl₁ has been identified asthe avoidance manoeuvre ΔVmax₁.{right arrow over (d)}₁₁ for obtainingthe lowest overall probability P_(g) of collision₁₁ in comparison withthe determination of all other estimated overall probabilities ofcollision P_(g) associated with the manoeuvre alternatives ΔV{rightarrow over (d)} performed from the reference orbit X_(ref) as describedin FIG. 7 . It will also be necessary to assume according to FIG. 8 thatthe overall probability P_(g) of collision₁₁ associated with said firstavoidance manoeuvre ΔVmax₁.{right arrow over (d)}₁₁ is greater than thecritical probability threshold of collision P_(thr). To this end, it isnecessary to determine at least one second avoidance manoeuvreΔVmax₁.{right arrow over (d)}_(5i) of the satellite 10 following thefirst avoidance manoeuvre ΔVmax₁.{right arrow over (d)}₁₁ so as toreduce the overall probability P_(g) of collision with the objective ofobtaining in the end an overall probability P_(g) of collision at leastequal to, or even less than, the critical probability threshold P_(thr)of collision. It will be necessary to name this second manoeuvre as thesecond avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) in thefollowing description of the invention.

According to FIG. 8 , a second avoidance orbit X_(5i) in continuity withthe first avoidance orbit X₁₁ is represented. This second orbit X_(5i),called second avoidance orbit X_(5i), follows the second avoidancemanoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) commanded at any of thefree slots Sl_(i) distinct from the first free manoeuvre slot Sl₁. Thefirst avoidance orbit X₁₁ of the satellite 10 at the manoeuvre timeinstant t_Sl_(i) before the second avoidance manoeuvre ΔVmax_(i).{rightarrow over (d)}_(5i) is directly determined, since it has beenpreviously determined according to the description in FIG. 7 . The firstavoidance orbit X₁₁ of the satellite 10 at the manoeuvre time instantt_Sl_(i) before the second avoidance manoeuvre ΔVmax_(i).{right arrowover (d)}_(5i) is denoted as X₁₁(t_Sl_(i)).

The determination of the second avoidance orbit X_(5i)(t_Sl_(i))evaluated at the manoeuvre time instant t_Sl_(i) following the secondavoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) can becalculated by updating the first orbit X₁₁(t_Sl_(i)) at the manoeuvretime instant t_Sl_(i) according to the second avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(5i). For Cartesian elements, thiscorresponds to the second avoidance manoeuvre ΔVmax_(i).{right arrowover (d)}_(5i) in the inertial reference frame. For Keplerian, circularand equinoctial elements, the Gaussian equation provides this deltastate. In all cases, the calculation of the orbital deviation created bythe second avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) canbe written: ΔX_(5i)(t_Sl_(i))=F(ΔVmax_(i).{right arrow over (d)}_(5i),X₁₁(t_Sl_(i))). In the same way as described in FIG. 4 , consideringthat the first orbit X₁₁ is a new reference orbit with respect to thesecond avoidance manoeuvre ΔVmax_(i).d_(5i), the orbital deviationΔX_(5i)(TCA_(i)) of the satellite 10 on each of the dates of closestpassages TCA_(i) can be determined according to the formula:

ΔX _(5i)(TCA _(i))=ϕ(TCA _(i) ,t_Sl _(i)).ΔX_(5i)(t_Sl _(i))=ϕ(TCA _(i),t_Sl ₁).ϕ(t_Sl _(i) ,t_Sl ₁)⁻¹. ΔX_(5i)(t_Sl _(i))

In order to be able to calculate all individual probabilities ofcollision Pi between the satellite 10 according to its second avoidanceorbit ΔX_(5i)(t_Sl_(i)) following the second avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(5i), and all debris d₁, d₂, d₃, d₄,d_(i) of the cloud according to their respective date of closest passageTCA_(i), it is necessary to determine the second avoidance orbitX_(5i)(t_Sl_(i)) on each of said dates of closest passages TCA_(i). Inthis respect, the first avoidance orbit X₁₁(TCA_(i)) can be determinedon each of the dates of closest passage TCA_(i) by interpolating thisfirst avoidance orbit X₁₁(TCA_(i)) into the ephemerides generatedaccording to each of the dates of closest passage TCA_(i). Finally, thesecond avoidance orbit X_(5i)(t_Sl_(i)) can be determined on each ofsaid dates of closest passages TCA_(i) according to the formula:

X _(5i)(TCAi)=X ₁₁(TCA _(i))+ΔX _(5i)(TCA _(i))

The second avoidance orbit X_(5i) of the satellite 10 after the secondavoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) as well as theorbital covariance COVTCA_(i) of the satellite 10 being determined oneach date of closest passage TCA_(i), the orbit of each piece of debrisd₁, d₂, d₃, d₄, d_(i) and their covariance on their date of closestpassage TCA_(i) being also known, the method for adjusting the orbitalpath of satellite 10 may comprise determining all the individualprobabilities of collision Pi between the satellite 10 according to itssecond consecutive orbit X_(5i) following the second avoidance manoeuvreΔVmax_(i).{right arrow over (d)}_(5i), and all debris d₁, d₂, d₃, d₄,d_(i) of the cloud according to their respective date of closest passageTCA_(i). To this end, the overall probability P_(g5i) of collisionrelated to the second avoidance manoeuvre ΔVmax_(i).{right arrow over(d)}_(5i) performed during said any of the free slots Sl_(i) distinctfrom the first manoeuvre slot Sl₁ can be calculated and compared with acritical probability threshold P_(th) of collision.

Similarly to FIG. 7 , the method for adjusting the orbital path of thesatellite 10 may comprise determining a plurality of other overallprobabilities P_(g) of collision according to a plurality of furthersecond alternative avoidance manoeuvres ΔV{right arrow over (d)} incombination with the first avoidance manoeuvre ΔVmax₁.{right arrow over(d)}₁₁, each representing an alternative of the second ΔVmax_(i).{rightarrow over (d)}_(5i) avoidance manoeuvre represented in FIG. 8 ; theseother second alternative avoidance manoeuvres ΔV{right arrow over (d)}being according to another free manoeuvre execution slot Sl_(i) and/oralong another manoeuvre direction {right arrow over (d)} than the secondavoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i) as representedin FIG. 8 . Each of the overall probabilities of collision P_(g) eachrelated to one of the other second alternative avoidance manoeuvresΔV{right arrow over (d)} can be compared with the critical probabilitythreshold P_(th) of collision and with all other overall probabilitiesof collision P_(g) related to the other second avoidance manoeuvresΔV{right arrow over (d)}.

To this end, according to FIG. 8 , under the hypothesis of at least oneoverall probability P_(g) of collision, related to a second avoidancemanoeuvre ΔV{right arrow over (d)} less than or equal to the criticalprobability threshold P_(th) of collision, it will be necessaryaccording to the invention and in a non-limiting manner, to be able todetermine the second avoidance manoeuvre ΔV{right arrow over (d)}enabling the avoidance of the collision of the satellite 10 with all thedebris d₁, d₂, d₃, d₄, d_(i) of the cloud according to at least one ofthe three strategies of the method for adjusting the orbital path of thesatellite 10 similar to the three strategies described in the precedingparagraphs relating to FIG. 7 .

In the case of an overall probability P_(g) strictly less than thecritical probability threshold P_(th) of collision after the applicationof the second avoidance manoeuvre ΔVmax_(i).{right arrow over (d)}_(5i)following the first avoidance manoeuvre ΔVmax_(i).{right arrow over(d)}₁₁, a reduction in the maximum velocity variation ΔV_(max) ispossible in order to obtain an overall probability P_(g) of collisionpreferably equal to, or even very close to, the critical probabilitythreshold P_(th) of collision. In this way, the energy required for theidentified second avoidance manoeuvre ΔV{right arrow over (d)} will bereduced to a minimum.

According to the invention, and in accordance with the description inFIG. 7 and FIG. 8 , the first avoidance manoeuvre and the secondavoidance manoeuvre may each be manoeuvres performed on any of the freeslots Sl_(i), the free slot Sl_(i) associated with the second avoidancemanoeuvre being distinct from that associated with the first avoidancemanoeuvre. More particularly, according to a strategy with two or moreavoidance manoeuvres, and it is possible, according to the method foradjusting the orbital path of the satellite 10, to determine a secondavoidance manoeuvre to be performed on a free slot Sl_(i) prior in timeto the free slot Sl_(i) of the first manoeuvre. In other words,according to the method for adjusting the orbital path of the satellite10, it is possible to determine a first avoidance manoeuvre to beperformed on a free slot Sl_(i) later in time than the free slot of thesecond avoidance manoeuvre Sl_(i), said second avoidance manoeuvre beingdetermined later than the first manoeuvre.

To this end, in general, a first orbit X₁(t) from a first avoidancemanoeuvre ΔVmax.{right arrow over (d)}₁ relating to the reference orbitX_(ref), determined on any of the free slots Sl_(i), serving as a newreference orbit relative to a second avoidance manoeuvre ΔV.{right arrowover (d)}₂, should be able to be evaluated also for the free slot orslots Sl_(i) prior to said any of the free slots Sl_(i) associated withthe first manoeuvre. To this end, and in general, the first avoidanceorbit X₁(t_Sl_(i)<t) at all manoeuvre time instants t_Sl_(i) relating tothe free slots prior to the first avoidance manoeuvre ΔVmax.{right arrowover (d)}₁ orbit is determined by interpolation of the ephemeridesrelated to the reference orbit X_(ref).

To this end, it will be necessary for the method for adjusting theorbital path of a satellite 10 to command the avoidance manoeuvres tothe satellite 10 not in the order of determination of the avoidancemanoeuvres, but according to a time sequential execution of manoeuvresaccording to the time location of free slots Sl_(i) associated with thedetermined collision avoidance manoeuvres.

According to FIG. 9 , a non-limiting example of the application of astrategy for determining free slots Sl₁, Sl_(i) and avoidance manoeuvresrequired to avoid a collision of the satellite 10 with the cloud ofdebris d₁, d_(i) is represented. To this end, a hypothesis is made that5 free manoeuvre slots Sl₁, Sl₂, Sl₃, Sl₄, Sl₅ are available in order tobe able to carry out the avoidance manoeuvres in such a way as to obtainan overall probability P_(g) of collision less than or equal to thecritical threshold P_(th) of collision. As a non-limiting example, thecritical threshold of collision P_(th) is set to P_(th)=0.0005.

According to FIG. 9 , three lines representative of three determinationsD1, D2, D3 of three avoidance manoeuvres required for collisionavoidance between the satellite 10 and the cloud of debris d₁, d_(i) arerepresented. A fourth determination line D4 represents the optimisationof the parameters of the third manoeuvre, that is, the velocityvariation ΔV and the direction {right arrow over (d)} of the thrust soas to obtain an overall probability P_(g) of collision equal to thecritical threshold P_(th) of collision, equal to P_(th)=0.0005.

The first determination D1 consists in determining a first avoidancemanoeuvre ΔV.{right arrow over (d)} on any of the five free manoeuvreslots Sl₁, Sl₂, Sl₃, Sl₄, Sl₅ enabling a first lowest overallprobability to be obtained. To this end, in a manner similar to thatdescribed through FIG. 7 , a plurality of manoeuvres on each free slot,each along a plurality of directions related to the manoeuvre thrust andaccording to a maximum velocity variation ΔV related to each freemanoeuvre slot Sl₁, Sl₂, Sl₃, Sl₄, Sl₅ is evaluated. According to thisfirst determination D1, the first manoeuvre to obtain the first lowestoverall probability P_(g1) of collision is one of the manoeuvresevaluated on the third free slot Sl₃, along a first direction {rightarrow over (d)}₃ and according to the maximum velocity variation ΔV3maxallowed during the third free slot Sl₃. As a non-limiting example, thefirst overall probability P_(g1) of collision obtained has a value equalto P_(g1)=0.001. As this value of first overall probability P_(g1)following the first avoidance manoeuvre ΔV3max.{right arrow over(d)}₃={right arrow over (ΔV3)}max is not less than or equal to thecritical threshold of P_(th) of collision, a second collision avoidancemanoeuvre has to be determined.

According to FIG. 9 , the second determination D2 consists indetermining a second avoidance manoeuvre ΔV.{right arrow over (d)} onany of the four free manoeuvre slots Sl₁, Sl₂, Sl₄, Sl₅ distinct fromthe third slot already determined for the first avoidance manoeuvre{right arrow over (ΔV3)}max enabling a second lowest overall probabilityP_(g2) to be obtained, by taking account of the effect of the firstmanoeuvre {right arrow over (ΔV3)}max. To this end, in a manner similarto that described through FIG. 8 , a plurality of avoidance manoeuvreson each of the four free manoeuvre slots Sl₁, Sl₂, Sl₄, Sl₅ remainingavailable, is evaluated along a plurality of directions related to themanoeuvre thrust and according to a maximum velocity variation ΔVrelated to each free manoeuvre slot Sl₁, Sl₂, Sl₄, Sl₅ remaining.According to this second determination D2, the second avoidancemanoeuvre enabling the second lowest overall probability P_(g2) ofcollision to be obtained is one of the avoidance manoeuvres evaluated onthe second free slot Sl₂, along a second direction {right arrow over(d)}2 and according to the maximum velocity variation ΔV2max allowedduring the second free slot Sl₂. As a non-limiting example, the secondoverall probability P_(g2) of collision obtained has a value equal toP_(g2)=0.0007. As this value of second overall probability P_(g2)following the combination of the first manoeuvre {right arrow over(ΔV3)}max and the second avoidance manoeuvre {right arrow over (ΔV2)}maxis not less than or equal to the critical threshold of collision P_(th),a third collision avoidance manoeuvre has to be determined.

According to FIG. 9 , the third determination D3 consists in determininga third avoidance manoeuvre ΔV.{right arrow over (d)} on any of thethree free manoeuvre slots Sl₁, Sl₄, Sl₅ still available, enabling athird lowest overall probability P_(g3) to be obtained by taking accountof the combined effect of the first avoidance manoeuvre {right arrowover (ΔV3)}max and the second avoidance manoeuvre {right arrow over(ΔV2)}max. To this end, in a manner similar to that described throughFIG. 8 , a plurality of avoidance manoeuvres on each of the three freemanoeuvre slots Sl₁, Sl₄, Sl₅ remaining available, is evaluated along aplurality of directions related to the thrust of the avoidance manoeuvreand according to a maximum velocity variation ΔV related to each freemanoeuvre slot Sl₁, Sl₄, Sl₅ remaining. According to this thirddetermination D3, the third avoidance manoeuvre enabling the lowestthird overall probability P_(g3) of collision to be obtained is one ofthe manoeuvres evaluated on the fifth free slot Sl₅, along a fifthdirection {right arrow over (d)}5 and according to a maximum velocityvariation ΔV5max allowed during the fifth free slot Sl₅. As anon-limiting example, the third overall probability P_(g3) of collisionobtained has a value equal to P_(g2)=0.0003, that is, a value below thecritical threshold of P_(th) of collision.

According to FIG. 9 , a fourth determination D4 consists in adjustingthe parameters of the third manoeuvre so as to obtain a third overallprobability P_(g3) of collision equal to the critical threshold ofP_(th) of collision, namely P_(th)=0.0005. In this respect, a velocityvariation value ΔV5_(opt) less than the maximum velocity variationΔV5max allowed, and combined with a fifth direction {right arrow over(d)}5_opt optimised with respect to the optimal velocity variationΔV5_(opt) is obtained.

According to FIG. 9 , a collision avoidance command C of the satellite10 with all the debris d₁, d_(i) of the cloud comprises the combinationof the three determined avoidance manoeuvres {right arrow over(ΔV3)}max, {right arrow over (ΔV2)}max, {right arrow over (ΔV5)}_(opt)performed according to a time order related to the three free slotsassociated with said three manoeuvre. In other words, the collisionavoidance command C includes a first command C1 comprising the executionduring the second free slot Sl₂ of the second determined avoidancemanoeuvre {right arrow over (ΔV2)}max, then the collision avoidancecommand C includes a second command C2 comprising the execution duringthe third free slot Sl3 of the first determined avoidance manoeuvre{right arrow over (ΔV3)}max, and finally, the collision avoidancecommand C includes a third command C3 comprising the execution duringthe fifth free slot Sl₅ of the third determined avoidance manoeuvre{right arrow over (ΔV5)}_(opt).

Optionally, and according to the invention, in order to confirm theresult obtained, namely the determination of manoeuvres of the satelliteenabling collision avoidance between the satellite and all the debris ofthe cloud, preferably a numerical calculation of the path of thesatellite 10 including all the identified manoeuvres can be performed.

Indeed, the propagation used to evaluate the avoidance manoeuvres on theoverall probability P_(g) of collision, called fast propagation based onthe ephemeris of the state transition matrix ϕ(t, t₀) and on theephemeris of the reference orbit X_(ref) of satellite 10, is asimplified propagation. As a result, the overall probability P_(g) ofcollision may be slightly different from an overall probability ofcollision determined according to numerical orbit propagationdeterminations, for example and in a non-limiting manner, from theorbital parameters of satellite 10. To ensure that this overallprobability P_(g) of collision is close to the critical probabilitythreshold of collision P_(th), a numerical propagation taking account ofthe previously estimated manoeuvres should be performed and the overallprobability of collision recalculated.

If, however, the operation of calculating the overall probability P_(g)of collision based on a numerical propagation of the orbit of thesatellite 10, especially comprising the avoidance manoeuvres determinedpreviously, results in an overall probability P_(g) of collision greaterthan the critical probability threshold P_(th) of collision, it would benecessary, according to the invention, to resume the determination ofadditional avoidance manoeuvres according to the method for adjustingthe orbital path of the satellite 10 described in FIGS. 7 and 8 , from anew reference orbit relating to the orbit of the satellite determinednumerically.

A simpler solution than that based on a verification of the calculationof the overall probability P_(g) of collision by a numerical calculationof the propagation of the orbit of the satellite corrected according tothe avoidance manoeuvres determined previously, simply consists insetting a sufficiently low critical probability threshold of collisionP_(th) in order to compensate for the uncertainties of the so-calledfast propagation solution.

According to FIG. 10 , a non-limiting example of a flowchart relating tothe method 100 for adjusting the orbital path of the satellite 10comprises several steps.

The first step consists in determining 110 a reference path of the orbitX_(ref) of the satellite 10 from an initial time instant t₀ until thedate of closest passage TCA₁, TCA_(i) furthest from the initial timeinstant t₀. Preferably, according to the invention, the determination110 of the reference path of the orbit X_(ref) of the satellite 10 isdetermined according to a free drift propagation of the orbit X_(ref) ofthe satellite 10.

The first step is associated with a second step relating to thedetermination 120 of an ephemeris of a state transition matrix ϕ(t, t₀)representative of the reference path of the orbit X_(ref) of thesatellite 10. This first step is essential to the invention. It makes itpossible especially to calculate all the state transition matricesϕ(t_(n), tm) required for the method for adjusting the orbital path ofthe satellite.

The determined state transition matrix ϕ(t, t₀) enables a step 130 ofpropagating at least one first alternative orbit X_(1i) of the referenceorbit X_(ref) of the satellite 10 according to at least one firstavoidance manoeuvre ΔV.{right arrow over (d)} related to the satellite10 performed during at least one free manoeuvre time slot Sl₁, and fromat least one manoeuvre time instant t_Sl₁ of the at least one freemanoeuvre time slot Sl₁ until the date of closest passage TCA_(i)furthest from the initial time instant t₀.

The propagation of the at least one first alternative orbit X_(1i) ofthe satellite 10 enables a step of analytically determining 140 anindividual probability P_(i) of collision on each date of closestpassage TCA₁, TCA_(i) for each piece of debris d₁, d_(i) related to atleast the first alternative orbit X_(1i) of the satellite 10.

The method 100 for adjusting the orbital path of the satellite 10, inaccordance with the description in FIG. 3 , comprises a step ofdetermining 150 at least one overall probability P_(g) of collisionaccording to all the individual probabilities P_(i) of collisiondetermined according to the at least one first alternative orbit X_(1i)of the satellite 10 related to the at least one first avoidancemanoeuvre ΔV.{right arrow over (d)}. This step of determining 150 atleast one overall probability P_(g) of collision is followed by a stepof selecting 160 at least one first lowest overall probability P_(g) ofcollision from the at least one determined overall probability P_(g) ofcollision.

Preferably, the method 100 comprises an initial step according to whicheach avoidance manoeuvre ΔV.{right arrow over (d)} comprises an initialvalue of maximum velocity variation ΔVmax allowed during the avoidancemanoeuvre ΔV.{right arrow over (d)}. The method 100 preferably alsocomprises a step of adjusting 170 the velocity variation ΔV of the atleast one first avoidance manoeuvre ΔV.{right arrow over (d)} when theselected at least first lowest overall probability P_(g) is less than acritical probability threshold P_(th) of collision, so as to obtain atleast one first overall probability P_(g) of collision as close aspossible to or equal to the critical probability threshold P_(th) ofcollision. The adjustment of the velocity variation ΔV may also beassociated with an adjustment of the direction {right arrow over (d)} ofthe manoeuvre.

The method also includes a step of determining 180 a command C of thesatellite 10 including at least the first manoeuvre related to the firstlowest overall probability P_(g) of collision selected so as to bestminimise the risk of collision of the satellite 10 with the cloud ofdebris.

Preferably, the step of propagating 130 alternative orbits is repeatedseveral satellite times by a step of multiple iterations 190 on thedirection {right arrow over (d)} of the avoidance manoeuvre ΔV.{rightarrow over (d)} so as to obtain a first plurality of alternative orbitsX_(1i) related to a first plurality of avoidance manoeuvres ΔV.{rightarrow over (d)} and to evaluate a first plurality of overallprobabilities of collision P_(g) related to each of the alternativeorbits related to the first plurality of avoidance manoeuvres ΔV.{rightarrow over (d)}.

Preferably, the step of propagating 130 alternative orbits is alsorepeated several times by a step of multiple iterations 200 according toa plurality of free manoeuvre slots Sl₁, Sl_(i) of the satellite 10 soas to obtain a second plurality of alternative orbits X_(1i) and toevaluate a second plurality of overall probabilities P_(g) of collisionsrelated to the second plurality of alternative orbits X_(1i).

According to FIG. 10 , the step of determining 180 a command C of thesatellite 10 may comprise a plurality of additional steps 230, 240, 250,260, 270, 290, and 300 similar to the steps preceding the step ofdetermining 180 a command C, for defining a step of determining 280 thecommand C of the satellite 10 for which at least one second avoidancemanoeuvre combined with the first manoeuvre related to the first lowestoverall probability P_(g) of collision is also determined. The at leastone second manoeuvre is the second manoeuvre related to a second lowestprobability of collision determined according to the steps 230, 240,250, 260, 270, 290, and 300 of the method.

According to FIG. 10 , the step of determining 280 the command C of thesatellite 10 for which at least one second avoidance manoeuvre combinedwith the first manoeuvre related to the first lowest overall probabilityP_(g) of collision is also determined, may include the steps 210, 220 ofthe method for which the reference path of the satellite 10 is the pathof the first alternative orbit X_(1i) of the satellite 10 related to thefirst lowest overall probability P_(g) of collision. The path of thefirst alternative orbit X_(1i) of satellite 10 could be numericallyre-evaluated taking account of the first avoidance manoeuvre. The pathof the first alternative orbit X_(1i) of satellite 10 will serve as anew reference path, and enable the generation of new ephemerides of thestate transition matrix ϕ(t, t₀).

According to FIG. 11 , a device 400 for implementing the method foradjusting the orbital path of the satellite 10 may comprise aninformation processing unit 402 of the processor type such as, forexample and in a non-limiting manner, a processor specialised in signalprocessing, or a microcontroller, or any other type of circuit enablingsoftware-type instructions to be executed. The device 400 also includesrandom access memory 404 associated with the information processing unit402. The information processing unit 402 is configured to execute aprogram, also called a computer program, comprising instructionsimplementing the method 100 for adjusting the orbital path of asatellite 10 described above. The instructions are loaded into therandom access memory of the device 400 from any type of storage media406 such as, for example and in a non-limiting manner, a non-volatiletype memory or an external memory such as a removable storage memorycard. The instructions may also be loaded via a connection to acommunications network.

Alternatively, the computer program, comprising instructionsimplementing the method 100 for adjusting the orbital path of thesatellite 10, may also be implemented in hardware form by a machine orby an application-specific integrated circuit or by a programmable logicarray type electronic circuit.

It should be understood that the detailed description of the subjectmatter of the invention, which is given for illustrative purposes only,does not in any way constitute a limitation, as the technicalequivalents are also comprised in the scope of the present invention.

1. A method for adjusting the orbital path of a satellite to limit arisk of collision with a cloud of space debris, each piece of debrisbeing associated to a date of closest passage with the satellite, themethod including the steps of: (a) determining a reference path of theorbit of the satellite from an initial time instant until the date ofclosest passage furthest from the initial time instant; (b) determiningan ephemeris of state transition data representative of the referencepath of the orbit of the satellite; (c) propagating, according to thedetermined ephemeris of the state transition data, at least one firstalternative orbit of the reference orbit of the satellite according toat least one first avoidance manoeuvre related to the satelliteperformed during at least one free manoeuvre time slot, and from atleast one manoeuvre time instant of the at least one free manoeuvre timeslot until the date of closest passage furthest from the initial timeinstant; (d) analytically determining an individual probability ofcollision on each date of closest passage for each piece of debrisaccording to the at least one first alternative orbit of the satellite;(e) determining at least one overall probability of collision accordingto all the individual probabilities of collision determined according tothe at least one first alternative orbit of the satellite related to theat least one first avoidance manoeuvre; (f) selecting at least one firstlowest overall probability of collision among the at least one overallprobability obtained according to step (e); (h) determining a command ofthe satellite including at least the first manoeuvre related to theselected first lowest overall probability of collision.
 2. The methodaccording to claim 1, wherein determining a reference path of the orbitof the satellite is determined according to a free drift propagation ofthe orbit of the satellite.
 3. The method according to claim 1, whereinthe steps (c), (d) and (e) are iteratively repeated along a plurality ofdirections of the at least one first avoidance manoeuvre so as to obtaina first plurality of alternative orbits related to a first plurality ofavoidance manoeuvres and to evaluate a first plurality of overallprobabilities of collision related to each of the alternative orbitsrelated to the first plurality of avoidance manoeuvres.
 4. The methodaccording to claim 1, wherein each avoidance manoeuvre comprises aninitial value of maximum velocity variation allowed during the avoidancemanoeuvre.
 5. The method according to claim 1, further comprising a step(g), preceding step (h), comprising an adjustment of a velocityvariation of the at least one first avoidance manoeuvre of the commandwhen the at least one first lowest overall probability selected in step(f) is less than a critical probability threshold of collision, so as toobtain at least one first overall probability of collision as close aspossible to or equal to the critical probability threshold of collision.6. The method according to claim 1, wherein the steps (c), (d) and (e)are repeated according to a plurality of free manoeuvre time slots ofthe satellite so as to obtain a second plurality of alternative orbitsand to evaluate a second plurality of overall probabilities of collisionrelated to the second plurality of alternative orbits.
 7. The methodaccording to claim 1, wherein the step (h) comprises a step of:determining at least one second manoeuvre of the command of thesatellite, the second manoeuvre being combined with the first manoeuvrerelated to the first lowest overall probability of collision, the atleast one second manoeuvre producing a second alternative orbit enablingthe calculation of a second lowest probability of collision according tothe steps (c) to (f) of the method.
 8. The method according to claim 7,wherein determining the second manoeuvre of the command of thesatellite, includes the steps (a) and (b) of the method according towhich the reference path of the satellite is the path of the firstalternative orbit of the satellite related to the first lowest overallprobability of collision.
 9. The method according to claim 1, whereinthe ephemeris of state transition data is an ephemeris of statetransition matrix.
 10. (canceled)
 11. An information storage mediumstoring a computer program comprising instructions for implementing, bya processor, the method according to claim 1, when the program is readand executed by the processor.